Network management based on assessment of topological robustness and criticality of assets

ABSTRACT

A system and method of managing a network that includes assets are described. The method includes modeling the network as a directed graph with each of the assets represented as a node and determining alternative paths to each node from each available corresponding source of the node. The method also includes computing upstream robustness of each node, computing upstream robustness of the network, and computing downstream criticality of each node. Managing the network and each asset of the network is based on the upstream robustness and the downstream criticality of each node.

BACKGROUND

The present invention relates to network management, and morespecifically, to network management based on assessment of thetopological robustness and criticality of assets.

There are many types of networks that include a number of assets thataffect each other. Exemplary networks with a number of interdependentassets include a power network (power grid), gas network, and a waternetwork. Reliability of such networks can depend not only on the assetsthemselves and their failure rates but also on the robustness of thenetwork topology. Assets of a given network can be of different typesand can be for different uses. For example, a power network includeselectrical assets (e.g., transformers, switches, fuses) andnon-electrical assets (e.g., support structures, poles).

SUMMARY

According to one embodiment of the present invention, a method ofmanaging a network that includes assets includes modeling, using aprocessor, the network as a directed graph with each of the assetsrepresented as a node; determining, using the processor, alternativepaths to each node from each available corresponding source of the node;computing upstream robustness of each node; computing upstreamrobustness of the network; computing downstream criticality of eachnode; and managing the network and each asset of the network based onthe upstream robustness and the downstream criticality of each node.

According to another embodiment, a network management system to manageassets of the network includes a memory device configured to storeinstructions, and a processor configured to process the instructions tocompute upstream robustness of each node, compute upstream robustness ofthe network, compute downstream criticality of each node, and to managethe network based on the upstream robustness and the downstreamcriticality of each node.

According to yet another embodiment, a computer program product includesa tangible storage medium readable by a processing circuit and storinginstructions for execution by the processing circuit to perform a methodof managing a network that includes assets. The method includes modelingthe network as a directed graph with each of the assets represented as anode; determining alternative paths to each node from each availablecorresponding source of the node; computing upstream robustness of eachnode; computing upstream robustness of the network; computing downstreamcriticality of each node; and managing the network and each asset of thenetwork based on the upstream robustness and the downstream criticalityof each node.

Additional features and advantages are realized through the techniquesof the present invention. Other embodiments and aspects of the inventionare described in detail herein and are considered a part of the claimedinvention. For a better understanding of the invention with theadvantages and the features, refer to the description and to thedrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The subject matter which is regarded as the invention is particularlypointed out and distinctly claimed in the claims at the conclusion ofthe specification. The forgoing and other features, and advantages ofthe invention are apparent from the following detailed description takenin conjunction with the accompanying drawings in which:

FIG. 1 is a process flow of a method of managing a network based ondetermining upstream robustness and downstream criticality according toembodiments;

FIG. 2 is an exemplary graph used to identify nodes and connections forembodiments of the invention;

FIG. 3 shows the processes involved in computing upstream robustness atblock 130 (FIG. 1) according to an embodiment; and

FIG. 4 is a block diagram of a processing system to implementembodiments of the invention.

DETAILED DESCRIPTION

As noted above, topological robustness can affect network reliability inaddition to failure rate of assets within the network. Topologicalrobustness of the network refers to whether multiple sources areavailable to a given asset such that, if one fails, the other(s) cancontinue to supply the asset, for example. A lack of robustnessincreases criticality of an asset. That is, for example, the only assetsupplying several downstream assets is more critical than one of severalassets supplying a downstream asset. The interplay between robustnessand criticality, therefore, effects the management of the network. Aless robust and more critical asset may require more frequentinspection, for example. Embodiments of the methods and systemsdescribed herein relate to determining upstream robustness as well asdownstream criticality in order to manage the network and its assets.While an electrical network (grid) is discussed for exemplary purposes,the description herein applies to any network with interdependentassets.

FIG. 1 is a process flow of a method of managing a network based ondetermining upstream robustness and downstream criticality according toembodiments detailed below. Throughout the discussion herein, asset andnode are used interchangeably because the representation of the assetsin a directed graph is as nodes. At block 110, modeling the network as adirected graph includes indicating the assets of the network as nodesand showing the interconnection among the nodes as edges or paths whichare further detailed below. Determining alternative paths to each targetnode from available sources, at block 120, leads to computing theupstream robustness of each target node at block 130. At block 140,upstream robustness of the network is computed. At block 140, anadditional set of key performance indicators (KPIs) used for robustnessassessment are also computed. At block 150, computing downstreamcriticality for each target node is performed along with computing anadditional set of KPIs for assessment of asset criticality. Managing thenetwork at block 160 involves examining the robustness and criticalitydetermined at the previous processes. Each of these processes is furtherdetailed below.

FIG. 2 is an exemplary graph 200 used to identify nodes 210 andconnections 220 for embodiments of the invention. Several nodes 210 areshown with connections 220 indicating the physical topology of thenetwork. Steps involved in the generation of the graph 200 are known andare not detailed here. Generally, the physical topology is convertedinto a list of edges. Each edge is an ordered pair of two assets, and itis assumed that electric power flows between the pair of assets. Theassets are represented by the nodes 210 and the connectivity 220 isdefined by the edges. The nodes 210 may be classified in one of threecategories: source assets that serve as the source of all electricalpower in the grid, auxiliary assets (e.g., cables, poles, switches,protection devices) that are critical to delivery of electrical power tosink assets, and the sink assets that directly serve customers. In theexemplary graph 200, the nodes 210 include a source asset—source pp—asink asset—endpoint s2—and auxiliary assets—cables c1-c6, transformerst1 -t3, and open point ol. While the exemplary graph 200 pertains to apower network (grid), the embodiments detailed herein are not limited toa power network, as noted above.

Determining the set of alternate paths (at block 120) Pt from the sourcenodes to each of the target nodes t includes using a breadth-firstsearch (BFS). The BFS involves traversing the graph (e.g., 200 in FIG.2) by beginning with the source node (e.g., pp in FIG. 2) andprogressing through the nodes (210, FIG. 2) one-at-a-time from the rootto its neighbors. The set Pt is given by:P_(t)={P_(t,1), P_(t,2), . . . P_(t,m)}  [EQ. 1]The number of paths to the target node t is m. For the i^(th) path inthe set Pt, which represents a length of l (1 number of assets) from thesource asset to the target node t,P_(t,i)={a₁, a₂, . . . a_(l)}  [EQ. 2]Each element in the Pt set represents a path Pt,i, and each path Pt,iincludes a set of intervening assets.

FIG. 3 shows the processes involved in computing upstream robustness atblock 130 (FIG. 1) according to an embodiment. Generally, the processesinclude computing inter-path independency of each alternative path Pt,iin Pt 305, computing intra-path independency of the target node t ineach alternative path Pt,i in Pt 345, and computing the upstreamrobustness for each target node t based on the inter-path independencyand the intra-path independency 370. Each of these processes if furtherdetailed herein. At block 310, computing the universe Ut of assetsbetween the target node t and the sources is as follow:U_(t)={P_(t,1)∪P_(t,2)∪. . . ∪P_(t,m)}  [EQ. 3]Ut is the union of the paths in the set Pt. Determining the frequency ofoccurrences fc of each asset t in Ut, at block 320, is given by:

$\begin{matrix}{f_{c} = \begin{Bmatrix}{{f_{c} + 1},{{ifc} \in P_{t,i}}} \\{f_{c},{{ifc} \notin P_{t,i}}}\end{Bmatrix}} & \left\lbrack {{EQ}.\mspace{14mu} 4} \right\rbrack\end{matrix}$Computing the score sc of each component t in Ut is based on the scorebeing an inverse of the frequency:

$\begin{matrix}{s_{c} = \frac{1}{f_{c}}} & \left\lbrack {{EQ}.\mspace{14mu} 5} \right\rbrack\end{matrix}$Then, at block 340, computing the inter-path independency of a path Pt,iis based on summing the score of each component in the path andnormalizing with the length of the path Lt,i:

$\begin{matrix}{{PI}_{t,i}^{inter} = {\frac{1}{L_{t,i}}{\sum\limits_{i \in P_{t,i}}s_{i}}}} & \left\lbrack {{EQ}.\mspace{14mu} 6} \right\rbrack\end{matrix}$

At block 350, determining the length of the path Pt,i in terms of thenumber of components in the path is based on the cardinality (number ofelements) of the path (set) Pt,i and is given by:L _(t,i) =|P _(t,i)|  [EQ. 7]Then, at block 360, computing the intra-path independency of a targetnode t in a path Pt,i is as a function of the length of the pathdetermined from EQ. 7.

$\begin{matrix}{{PI}_{t,i}^{intra} = \frac{1}{L_{t,i} + 1}} & \left\lbrack {{EQ}.\mspace{14mu} 8} \right\rbrack\end{matrix}$The “+1” in the denominator is included to include the target node t,because the target node t may fail, as well. Once the inter-pathindependency (at block 340, based on blocks 310-340) and the intra-pathindependency (at block 360, based on blocks 350 and 360) are computed,upstream robustness of the target node t is computed, at block 370, as:

$\begin{matrix}{R_{{ups}\;}^{t} = {\sum\limits_{i = 1}^{m}{{PI}_{t,i}^{inter}{PI}_{t,i}^{intra}}}} & \left\lbrack {{EQ}.\mspace{14mu} 9} \right\rbrack\end{matrix}$The number of alternative paths to the target node t is m. As EQ. 9indicates, the upstream robustness is a function of the level ofdisjointedness between all alternative paths to the target node t(represented by the inter-path independency) and the number ofcomponents on which the target node t depends to reach a source in eachof these paths (represented by intra-path independency). That is, themore disjointed the alternative paths are (such that a failure in one isless likely to affect another) and the fewer components between thetarget node t and each source of each path (such that there are fewerchances of the path to the source being disrupted), the more robust thetarget node t is.

At block 140 (FIG. 1), computing upstream robustness of the network G isbased on the upstream vulnerability of individual assets of the networkG. For the network G with N assets (N target nodes in turn), the networkupstream robustness is given by:

$\begin{matrix}{R_{ups}^{G} = {\sum\limits_{i = 1}^{N}R_{ups}^{i}}} & \left\lbrack {{EQ}.\mspace{14mu} 10} \right\rbrack\end{matrix}$The network upstream robustness measures the aptitude of the network tocontinue operation (e.g., deliver electric power to nodes of the networkin the exemplary case of an electrical grid application). Thus, only therobustness of each asset is considered in computing the networkrobustness. Additional KPIs are also computed at block 140. The pathcount (PCt) of a target node t assesses the topological redundancy inreaching the target node t from available sources. The path countevaluates the total number of alternative paths to the target node tfrom the source(s) and is computed as the cardinality of Pt (determinedin EQ. 1) as:PC _(t) =|P _(t)|  [EQ. 11]The effective disjoint path count (EDPCt) of a target node t quantifiesthe effective number of independent paths from a source to the targetnode t. The EDPCt accounts for the disjointedness of each path Pt,i(from EQ. 2) in the set of paths Pt and is computed as a summation ofthe inter-path independency of each path from a source to the targetnode t:

$\begin{matrix}{{EDPC}_{t} = {\sum\limits_{i = 1}^{m}{PI}_{t,i}^{inter}}} & \left\lbrack {{EQ}.\mspace{14mu} 12} \right\rbrack\end{matrix}$The effective path length (EPLt) of a target node t gives the averageeffective distance to sources of the target node t in terms of thenumber of intervening assets. The EPLt is computed as a number of assetsper effective disjoint path between the target node t and its sources:

$\begin{matrix}{{EPL}_{t} = \frac{U_{t}}{{EPDC}_{t}}} & \left\lbrack {{EQ}.\mspace{14mu} 13} \right\rbrack\end{matrix}$

At block 150 (FIG. 1), downstream criticality is computed for eachtarget node t. Because, with respect to activity downstream of a givenasset, the asset is not a target (as it is for an upstream source), theterm component c is used rather than target node t. To determine thedownstream criticality of a component c of a network G, the component cis removed from the network to obtain a reduced network G′:G′=G\c  [EQ. 14]The network upstream robustness is computed for G′, the reduced network,based on the processing detailed above at blocks 110 through 140. Then,the downstream criticality of the component c is computed as a drop inthe network upstream robustness of the network G (see EQ. 10):

$\begin{matrix}{C_{down}^{c} = {\frac{\left( {R_{ups}^{G} - R_{ups}^{c}} \right) - R_{ups}^{G^{\prime}}}{\left( {R_{ups}^{G} - R_{ups}^{c}} \right)}*100}} & \left\lbrack {{EQ}.\mspace{14mu} 15} \right\rbrack\end{matrix}$The use of the robustness of the component c in both the numerator anddenominator acts as a correction factor to ensure that the downstreamcriticality of a leaf node is 0. A leaf node is one with no childrensuch that it has no effect on assets downstream of itself. AdditionalKPIs are also computed at block 150. The disconnection impact index(DIIt) of an asset t quantifies the impact of its removal from thenetwork from different perspectives. Consequences of the removal of anasset t can be measured based on different aspects (consequences of theremoval) including, for example, the number of disconnected assets, thenumber of disconnected customers (from the network), the amount of lostdemand, and the amount of lost revenue. Consequences represent the setof these and other consequences, ands_(t)={a₁, a₂, . . . a_(l)}  [EQ. 16]EQ. 16 indicates the set of assets that are disconnected upon removal ofthe asset t. Then DIIt is given by:

$\begin{matrix}{{DII}_{t} = {\sum\limits_{t \in s_{t}}{consequences}_{t}}} & \left\lbrack {{EQ}.\mspace{14mu} 17} \right\rbrack\end{matrix}$With regard to the consequences, for example, quantifying DIIt of anasset t in terms of the number of disconnected customers requiresevaluating the summation of the number of disconnected customers perdisconnected asset in the set of assets shown in EQ. 16.

Determining the upstream robustness and downstream criticality of theassets of the network, as well as the network as a whole facilitatesmanaging the network at block 160. The relative criticality of a givenasset may suggest a more or less frequent inspection and maintenanceperiod, for example. More critical assets may be inspected andmaintained more often than less critical assets. As another example, thesource of a less robust asset may be maintained more often than thesource of a more robust asset. The information may be used to upgradethe system, as well. For example, a redundant source may be added forhighly critical assets.

FIG. 4 is a processing system 400 configured to implement embodimentsdescribed herein. The processes detailed herein may be implemented byone or more processors (processing circuits) 410 based on instructionsstored in one or more memory devices 420. The memory devices 420 mayadditionally store data used in the processing. The instructions and oneor more memory devices 420 represent a computer program product toimplement the detailed processes. The processing system 400 mayadditionally include an input interface 430 (e.g., keyboard, wired orwireless communication link) to receive commands or data, as well as anoutput interface 440 (e.g., display device, communication link) to sendoutput. The computer program product (420) and processor 410 may bestand-alone components or may be integrated with other components of thenetwork.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the invention. Asused herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of onemore other features, integers, steps, operations, element components,and/or groups thereof.

The corresponding structures, materials, acts, and equivalents of allmeans or step plus function elements in the claims below are intended toinclude any structure, material, or act for performing the function incombination with other claimed elements as specifically claimed. Thedescription of the present invention has been presented for purposes ofillustration and description, but is not intended to be exhaustive orlimited to the invention in the form disclosed. Many modifications andvariations will be apparent to those of ordinary skill in the artwithout departing from the scope and spirit of the invention. Theembodiment was chosen and described in order to best explain theprinciples of the invention and the practical application, and to enableothers of ordinary skill in the art to understand the invention forvarious embodiments with various modifications as are suited to theparticular use contemplated

The flow diagrams depicted herein are just one example. There may bemany variations to this diagram or the steps (or operations) describedtherein without departing from the spirit of the invention. Forinstance, the steps may be performed in a differing order or steps maybe added, deleted or modified. All of these variations are considered apart of the claimed invention.

While the preferred embodiment to the invention had been described, itwill be understood that those skilled in the art, both now and in thefuture, may make various improvements and enhancements which fall withinthe scope of the claims which follow. These claims should be construedto maintain the proper protection for the invention first described.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

What is claimed is:
 1. A method of managing a network that includesassets, the method comprising: modeling, using a processor, the networkas a directed graph with each of the assets represented as a node;determining, using the processor, alternative paths to each node fromeach available corresponding source of the node; computing upstreamrobustness of each node; computing upstream robustness of the network;computing downstream criticality of each node; and managing the networkand each asset of the network based on the upstream robustness and thedownstream criticality of each node corresponding to each asset, whereinthe managing includes modifying a schedule for inspection of an asset.2. The method according to claim 1, further comprising classifying eachnode in the directed graph, wherein the classifying each node includesclassifying each node as a source asset, a target asset that directlyserves a customer of the network, or an auxiliary asset that delivers aresource of the network from to at least one target asset.
 3. The methodaccording to claim 1, wherein the computing the upstream robustness ofeach node includes computing inter-path independency and intra-pathindependency for each node.
 4. The method according to claim 1, whereinthe computing the upstream robustness of the network is based on theupstream robustness of each of the nodes.
 5. The method according toclaim 1, further comprising assessing topological redundancy of eachnode based on determining a total number of alternative paths to thenode from the sources of the node.
 6. The method according to claim 1,further comprising determining an effected disjoint path count of eachnode based on an inter-path independency of each path from the sourcesof the node to the node.
 7. The method according to claim 1, furthercomprising determining an average effective distance from the sources ofeach node to the node in terms of a number of intervening assets.
 8. Themethod according to claim 1, wherein the computing the downstreamcriticality of each node includes removing the node from the network togenerate a reduced network and determining upstream robustness of thereduced network.
 9. The method according to claim 8, further comprisingdetermining an impact of the removing the node based on a number ofdisconnected customers in the reduced network.
 10. The method accordingto claim 1, wherein the modifying comprises increasing inspectionfrequency of an asset corresponding to a first node when the first nodehas a lower upstream robustness than a second node or a higherdownstream criticality than a third node.
 11. The method according toclaim 1, wherein the network is an electric power network, and an edgebetween a pair of the nodes represents a flow of electric power betweena pair of the assets corresponding to the pair of nodes.
 12. The methodaccording to claim 1, wherein the network is gas network.
 13. The methodaccording to claim 1, wherein the network is a water network.
 14. Themethod according to claim 1, wherein the upstream robustness of eachnode is computed in accordance with the alternative paths.
 15. Themethod according to claim 1, wherein the upstream robustness of the eachnode is directly proportional to a disjointedness of the alternativepaths.
 16. The method according to claim 1, wherein the upstreamrobustness of the each node is inversely proportional to a number ofnodes between the each node and each source node of each of thealternative paths.
 17. The method according to claim 1, wherein theupstream robustness of the network measures an aptitude of the networkto continue operation.
 18. The method according to claim 1, wherein thedownstream criticality of the each node is computed as a drop in thenetwork upstream robustness resulting from a removal of the each node.19. The method according to claim 1, wherein the asset is a source of asecond asset having a low upstream robustness relative to other assetsof the assets.
 20. A method of managing a network that includes assets,the method comprising: modeling, using a processor, the network as adirected graph with each of the assets represented as a node;determining, using the processor, alternative paths to each node fromeach available corresponding source of the node; computing upstreamrobustness of each node in accordance with the alternative paths;computing upstream robustness of the network in accordance with theupstream robustness of the nodes; computing downstream criticality ofeach node in accordance with a removal of the each node from thedirected graph and a resulting upstream robustness of the network; andmodifying a schedule for inspection of an asset of the network based onthe upstream robustness and the downstream criticality of a nodecorresponding to the asset.